The use of the contiguity constraint is important only at the beginning of the aggregation procedure the higher-inner-flows constraint gives singleton regions, and the lower-variation constraint forces the biggest employment centre as an isolated region up to a relatively high level of aggregation.
The inclusion of constraints in the Intramax procedure was analysed by a programme code developed in Mathematica 10.3 by the processing time, by intra-regional shares of total flows, by self-containment indexes, by numbers of singleton and isolated regions, by the number of aggregation steps where a combination of constraints was applied, by the number of searching steps until the combination of constraints was satisfied, and by surveying the results geographically. the contiguity constraint, the higher-inner-flows constraint, and the lower-variation-of-inner-flows constraint. In this paper, we analyse the simultaneous use of three different constraints in the original Intramax procedure, i.e. Intramax is a hierarchical aggregation procedure for dealing with the multi-level specification problem and with the association issue of data set reduction, but it was used as a functional regionalization procedure many times in the past. It is demonstrated how the FER geography largely overcomes the spatial autocorrelation problem encountered in using de jure regions. The new national geography of FERs is described and this functional regional geography is then used to investigate aspects of regional labour market performance. These new functional regions should provide a much improved geography for the analysis of aspects of labour market performance which has relied largely on using data for de jure regions - such as Statistical Divisions and Local Government Areas - for which census and other data are available on which much of the research involving the spatial econometric modelling of labour market performance in Australia has relied which are far from ideal for such analyses.
The demarcation of FRRs, which are formed on spatial building blocks known as SLAs (Statistical Local Areas), uses a methodology that optimises within-region self- containment of commuting to jobs. A new geography of Functional Economic Regions (FERs) has been created across the large metropolitan city regions and across the non-metropolitan areas of the nation.